Generalization of an existence theorem for complementarity problems

Authors:
Qingjie Hu;Yu Chen;Jingtong Wang;Zi-Sheng Ouyang
Affiliations:
-;-;-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

In this paper, we present a new notion of exceptional d-regular mapping, which is a generalization of the notions of exceptional regular mapping and d-regular mapping. By using the new notion, we establish a new existence result for complementarity problems. Our results only generalize Karamardian's and Zhao's existence results (Theorem 3.1 in Karamardian (1972) [5], Theorem 3.8 in Harker et al. (1990) [2], Theorem 4.1 in Zhao and Isac (2000) [6], Theorem 3.1 in Zhao (1999) [13]). In our analysis, the notion of a new generalized exceptional family of elements for complementarity problems plays a key role.